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Friday Sep. 7, 2012
Marching into the weekend with "Rhapsody in Blue" by Pearl Kaufman. I couldn't find
Kaufman's version on YouTube but here's a good substitute. You should listen to
"Bumble Boogie" (Pearl Kaufman's version).
The first of the Optional Assignments is now online (copies of the assignment were
handed out in class) You don't have to do these assignments, but if you do you can earn
extra credit. The assignment is due next Friday (Sep. 14). To earn full credit you need to
make an sincere attempt at answering all the questions and you should have the
assignment done before coming to class.
The Practice Quiz has been graded and was returned in class today. The average was
66% which, as you can seen from the table below, is pretty typical.
MWF class
T Th class
F12
66%
??
F11
65%
65%
F10
60%
67%
F09
66%
68%
F08
64%
65%
If you weren't in class you can download a copy of the Practice Quiz. I would suggest
you do that so that you can become familiar with the quiz format. Here are answers to
the questions on the Practice Quiz.
Three mains topics were covered in class today.
1st some appreciation for how strong the force exerted by air pressure is. Then we'll try
to understand the basic principle of a mercury barometer used to measure atmospheric
pressure. Finally I'll try to convince you that air pressure just doesn't push downward but
also upward and sideways. We didn't have time for the 4th item on the list above.
Recent classes have featured a steel bar and 25 pounds of bricks.
All of the weight of the steel bar rested on 1 square inch of area. Even though the pile of
bricks was heavier, the weight was spread out over a greater area. As a result the
pressure at the bottom of bricks was less than 1 psi. You'd need 94 bricks, 470 pounds of
bricks, to produce 14.7 psi.
Sea level pressure, 14.7 psi, might not sound like much. But when you start to multiply
14.7 by all the square inches on your body it turns into 1000s of pounds of weight
(force). As the picture above shows, when you're lying on the beach there are 470
pounds of air pressing down on a 4" x 8" area of your chest.
Why isn't the person in the picture above crushed by the weight of the atmosphere above.
The answer is that the person's body pushes back with the same amount of force. Air
does the same thing. This is a topic that we will come back to at the end of the class
today.
The next topic is a short explanation of how a mercury barometer works. A mercury
barometer is used to measure atmospheric pressure and is really just a balance that can be
used to weigh the atmosphere. You'll find a messier version of what follows on p. 29 in
the photocopied Class Notes.
The instrument in the left figure above ( a u-shaped glass tube filled with a liquid of some
kind) is actually called a manometer and can be used to measure pressure difference. The
two ends of the tube are open so that air can get inside and air pressure can press on the
liquid. Given that the liquid levels on the two sides of the manometer are equal, what
could you about PL and PR?
The liquid can slosh back and forth just like the pans on a balance can move up and
down. A manometer really behaves just like a pan balance (pictured above at right) or a
teeter totter (seesaw). Because the two pans are in balance, the two columns of air have
the same weight. PL and PR are equal (but note that you don't really know what either
pressure is, just that they are equal).
Now the situation is a little different, the liquid levels are no longer equal. You probably
realize that the air pressure on the left, PL, is a little higher than the air pressure on the
right, PR. PL is now being balanced by PR + P acting together. P is the pressure produced
by the weight of the extra fluid on the right hand side of the manometer (the fluid that lies
above the dotted line). The height of the column of extra liquid provides a measure of the
difference between PL and PR.
Next we will just go and close off the right hand side of the manometer.
Air pressure can't get into the right tube any more. Now at the level of the dotted line the
balance is between Pair and P (pressure by the extra liquid on the right). If Pair changes,
the height of the right column, h, will change. You now have a barometer, an instrument
that can measure and monitor the atmospheric pressure.
Barometers like this are usually filled with mercury. Mercury is a liquid. You need a
liquid that can slosh back and forth in response to changes in air pressure. Mercury is
also very dense which means the barometer won't need to be as tall as if you used
something like water. A water barometer would need to be over 30 feet tall. With
mercury you will need only a 30 inch tall column to balance the weight of the atmosphere
at sea level under normal conditions (remember the 30 inches of mercury pressure units
mentioned earlier). Mercury also has a low rate of evaporation so you don't have much
mercury gas at the top of the right tube (there's some gas, it doesn't produce much
pressure, but it would poison you if you were to start to breath it).
Here is a more conventional barometer design. The bowl of mercury is usually covered
in such a way that it can sense changes in pressure but is sealed to keep poisonous
mercury vapor from filling a room.
Average sea level atmospheric pressure is about 1000 mb. The figure above (p. 30 in the
photocopied Class Notes) gives 1013.25 mb but 1000 mb is close enough in this class.
The actual pressure can be higher or lower than this average value and usually falls
between 950 mb and 1050 mb.
The figure also includes record high and low pressure values. Record high sea level
pressure values occur during cold weather. The TV weather forecast will often associate
hot weather with high pressure. They are generally referring to upper level high pressure
(high pressure at some level above the ground) rather than surface pressure.
Most of the record low pressure values have all been set by intense hurricanes (the
extreme low pressure is the reason these storms are so intense). Hurricane Wilma in
2005 set a new record low sea level pressure reading for the Atlantic, 882 mb. Hurricane
Katrina had a pressure of 902 mb. The following table lists some of the information on
hurricane strength from p. 146a in the photocopied ClassNotes. 3 of the 10 strongest N.
Atlantic hurricanes occurred in 2005.
Most Intense North Atlantic
Hurricanes
Most Intense Hurricanes
to hit the US Mainland
Wilma (2005) 882 mb
Gilbert (1988) 888 mb
1935 Labor Day 892 mb
Rita (2005) 895 mb
Allen (1980) 899
Katrina (2005) 902
1935 Labor Day 892 mb
Camille (1969) 909 mb
Katrina (2005) 920 mb
Andrew (1992) 922 mb
1886 Indianola (Tx) 925
mb
Note that a new all time record low sea level pressure was measured in 2003 inside a
strong tornado in Manchester, South Dakota (F4 refers to the Fujita scale rating, F5 is the
highest level on the scale). This is very difficult (and very hazardous) to do. Not only
must the instruments be built to survive a tornado but they must also be placed on the
ground ahead of an approaching tornado and the tornado must then pass over the
instruments.
And now the last topic of the day.
Pressure at any level in the atmosphere depends on (is determined by) the weight of the
air overhead. You might get the idea that pressure just pushes downward.
Air pressure is a force that pushes downward, upward, and sideways. If you fill a balloon
with air and then push downward on it, you can feel the air in the balloon pushing back
(pushing upward). You'd see the air in the balloon pushing sideways as well.
We were able to see this by placing a brick on top of a balloon. The balloon gets
squished but not flattened. It eventually pushes back with enough force to support the
brick.
Another helpful representation of air in the atmosphere might be a people pyramid.
If the bottom person in the stack above were standing on a scale, the scale would measure
the total weight of all the people in the pile. That's analogous to sea level pressure being
determined by the weight of the all the air above.
The bottom person in the picture above must be strong enough to support the weight of
all the people above. That is equivalent to the bottom layer of the atmosphere pushing
upward with enough pressure to support the weight of the air above.
The air pressure in the four tires on your automobile pushes pushes upward with enough
force to keep this 1000 or 2000 pound vehicle (my own personal vehicle) off the ground.
The air pressure also pushes downward, you'd feel it if the car ran over your foot.
This was a logical point to do a demonstration. A demo that tries to prove that air
pressure really does push upward as well as downward. Not only that but that the upward
force is fairly strong. The demonstration is summarized on p. 35 a in the ClassNotes.
Don't worry too much about the details above because there's a more detailed explanation
is below. At this point you should wonder why is it that the water in a balloon will fall
while the water in the wine glass does not.
Here's a little bit more detailed and more complete explanation of what is going on. First
the case of a water balloon.
The figure at left shows air pressure (red arrows) pushing on all the sides of the balloon.
Because pressure decreases with increasing altitude, the pressure from the air at the top of
the balloon pushing downward (strength=14) is a little weaker than the pressure from the
air at the bottom of the balloon that is pushing upward (strength=15). The two sideways
forces cancel each other out. The total effect of the pressure is a weak upward pressure
difference force (1 unit of upward force shown at the top of the right figure).
Gravity exerts a downward force on the water balloon. In the figure at right you can see
that the gravity force (strength=10) is stronger than the upward pressure difference force
(strength=1). The balloon falls as a result. This is what you know would happen if you
let go of a water balloon, it would fall.
In the demonstration a wine glass is filled with water. A small plastic lid is used to cover
the wine glass. The wine glass is then turned upside and the water does not fall out.
All the same forces are shown again in the left most figure. In the right two figures we
separate this into two parts. First the water inside the glass isn't feeling the downward
and sideways pressure forces (because they're pushing on the glass, they're included on
the right figure ). Gravity still pulls downward on the water but the upward pressure
force is able to overcome the downward pull of gravity. It can do this because all 15
units are used to overcome gravity and not to cancel out the downward pointing pressure
force. The net upward force is strong enough to keep the water in the glass.
The demonstration was repeated using a 4 Liter flash (more than a gallon of water, more
than 8 pounds of water). The upward pressure force was still able to keep the water in
the flask (much of the weight of the water is pushing against the sides of the flask which
the instructor was supporting with his arms).
I've added one small piece of additional material that we didn't have time to cover
in class.
What difference does it make if pressure decreases with increasing altitude or if pressure
pushes upward, downward, and sideways?
Hot air balloons can go up and come back down. I'm pretty sure you know what would
cause the balloon to sink. I suspect you don't know what causes it to float upward.
Gravity pulls downward on the balloon. The strength of this force will depend on
whether the air is hot low density air (light weight) or cold higher density air (heavier
air).
Pressure from the air surrounding the balloon is pushing against the top, bottom, and
sides of the balloon (the blue arrows shown above at right). Pressure decreases with
increasing altitude. The pressure at the bottom pushing up is a little higher than at the top
pushing down (the pressures at the sides cancel each other out). Decreasing pressure
with increasing altitude creates an upward pointing pressure difference force that opposes
gravity. It is this upward pressure difference force that can cause a balloon to float
upward.